You are right, of course. There was a famous massacre of Unionist Germans trying to get to Mexico so they could eventually join the Union Army.
http://en.wikipedia.org/wiki/Nueces_massacre
My point was that the huge majority of immigrants went to northern states, not that none went to the South.
My family has old letters from Confederate ancestors, and they were convinced they were fighting Hessian mercenaries, just as their grandfathers had in the Revolution.